Closed-Form Solutions For European And Digital Calls In The Hull And White Stochastic Volatility Model And Their Relation To Locally R-Minimizing And Delta Hedges

Christian-Oliver Ewald, Klaus Schenk-Hoppé and Zhaojun Yang

No 07-11, Swiss Finance Institute Research Paper Series from Swiss Finance Institute

Abstract: This paper derives an analytic expression for the distribution of the average volatility ds in the stochastic volatility model of Hull and White. This result answers a longstanding question, posed by Hull and White (Journal of Finance 42, 1987), whether such an analytic form exists. Our findings are applied to obtain closed-form solutions for European and Digital call option prices. The paper also provides an explicit solution for the Delta hedge of a European call. Moreover, it is proved that the Delta hedge under the minimal martingale measure coincides with the locally R-minimizing hedge in the model considered here.

Keywords: Stochastic volatility models; incomplete markets; Delta hedging; locally R-minimizing hedging strategies Malliavin calculus (search for similar items in EconPapers)
JEL-codes: C61 C63 G13 (search for similar items in EconPapers)
Pages: 22 pages
Date: 2007-08
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